Split Courant algebroids as $L_{\infty }$-structures

Abstract

We show that split Courant algebroids, i.e., those defined on a Whitney sum $A\oplus A^{\ast }$, are in a one-to-one correspondence with multiplicative curved $L_{\infty }$-algebras. This one-to-one correspondence extends to Nijenhuis morphisms and behaves well under the operation of twisting by a bivector.

25 pages. Minor corrections. To be published in Journal of Geometry and Physics